Chapter 5

Question 1

What is the mass conservation equation?

Answer 1

Mass flow in = Mass flow out

=> (rho.A.u)out - (rhi.A.u)in = change in mass flow in the volume.

Question 2

Equations for Qx, Qy and Qz? Should be able to derive these..

Answer 2

Qx = (∂(rho.u)/∂x).dV 
Qy = (∂(rho.v)/∂y).dV
Qz = (∂(rho.w)/∂z).dV

Question 3

What is Qx + Qy + Qz equal to?

Answer 3

= mass flow in - mass flow out

Question 4

Derive the mass conservation equation now in terms of density and partial derivatives?

Answer 4

∂rho/∂t + ∂(rho.u)/∂x + ∂(rho.v)/∂y + ∂(rho.w)/∂z = 0

Question 5

How can this equation be simplified for:

1. Incompressible flow
2. 2D flow field and incompressible
3. 1D flow field and incompressible?

Answer 5

1. rho = constant
   => ∂u/∂x +∂v/∂y +∂w/∂z =0
2. ∂u/∂x +∂v/∂y=0
3. ∂u/∂x = 0 => u1-u2/dx=0 => u1=u2